Remark 2 This definition of geometric ergodicity is slightly less standard
than an alternative definition in which \(M\)  is not assumed to be
integrable with respect to \(\Pi \) , but is assumed to be finite
\(\Pi \) -almost everywhere. While [1]}'s [1]} Proposition
2.1 shows that the two definitions are actually equivalent, the
geometric convergence rates under the two definitions are not
necessarily equal.

